Chapter 6.4, Problem 3GP

Solution

To find: The margin of error for the provided survey. Also, compute the number of people that are required to reduce the margin of error to $\pm 2\%$

The margin of error is 0.02884.

The sample size is 2500.

Given:

Number of people = 1202

Margin of error $=\pm 2\%$

Calculation:

The margin of error is calculated as:

  $\begin{array}{c}\text{Margin of error}=\frac{1}{\sqrt{\text{Sample size}}}\\ =\frac{1}{\sqrt{1202}}\\ =\text{0}\text{.02884}\end{array}$

The sample size is calculated as:

  $\begin{array}{c}\text{Margin of error}=\frac{1}{\sqrt{\text{Sample size}}}\\ \pm 0.02=\frac{1}{\sqrt{\text{Sample size}}}\\ \frac{1}{\text{Sample size}}=0.0004\\ \text{Sample size}=2500\end{array}$

The required sample size is 2500.